Lyapunov exponents for truncated unitary and Ginibre matrices
Abstract
In this note, we show that the Lyapunov exponents of mixed products of random truncated Haar unitary and complex Ginibre matrices are asymptotically given by equally spaced `picketfence' statistics. We discuss how these statistics should originate from the connection between random matrix products and multiplicative Brownian motion on $\operatorname{GL}_n(\mathbb{C})$, analogous to the connection between discrete random walks and ordinary Brownian motion. Our methods are based on contour integral formulas for products of classical matrix ensembles from integrable probability.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.07375
 Bibcode:
 2021arXiv210907375A
 Keywords:

 Mathematics  Probability;
 Mathematical Physics
 EPrint:
 10 pages, comments welcome!